Question

the angles of a quadrilateral are in the ration 2 isto 3 isto 5isto 8 isto. find the smallest angle​

Answer 1

Correct Question :-

The angles of a quadrilateral are in the ratio of 2:3:5:8. Find the smallest angle.

Answer :-

The smallest angle is 40°.

Step-by-step explanation

To Find :-

• The smallest angle of quadrilateral.

★ Solution

Given,

The angles of quadrilateral are in the ratio of 2:3:5:8.

Assumption

Let us assume the angles of quadrilateral as 2x, 3x, 5x and 8x.

We know,

Sum of all interior angles of quadrilateral measures 360°

∴ 2x + 3x + 5x + 8x = 360

⇒ 2x + 3x + 5x + 8x = 360

⇒ 5x + 5x + 8x = 360

⇒ 10x + 8x = 360

⇒ 18x = 360

⇒ x = 360/18

⇒ x = 20

We got, The value of x as 20.

Therefore,

The angles of quadrilateral are :-

⇒ 2x = 2*20 = 40°

⇒ 3x = 3*20 = 60°

⇒ 5x = 5*20 = 100°

⇒ 8x = 8*20 = 160°

The angles are 40°, 60°, 160° and 160°.

Now, According the question,

• The smallest angle is :-

⇒ 40° > 60° > 100° > 160°

Hence, The smallest angle is 40°.